SUPPLEMENTS
PREFACE
CHAPTER 1 Introduction
1.1 The Origins of Operations Research
1.2 The Nature of Operations Research
1.3 The Impact of Operations Research
1.4 Algorithms and OR Courseware
Selected References
Problems
CHAPTER 2 Overview of the OperationsOverview of the Operations Research Modeling Approach
2.1 Defining the Problem and Gathering Data
2.2 Formulating a Mathematical Model
2.3 Deriving Solutions from the Model
2.4 Testing the Model
2.5 Preparing to Apply the Model
2.6 Implementation
2.7 Conclusions
Selected References
Problems
CHAPTER 3 Introduction to Linear Programming
3.1 Prototype Example
3.2 The Linear Programming Model
3.3 Assumptions of Linear Programming
3.4 Additional Examples
3.5 Formulating and Solving Linear Programming Models on a Spreadsheet
3.6 Formulating Very Large Linear Programming Models
3.7 Conclusions
Selected References
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Problems
Case 3.1 Auto Assembly
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Case 3.2 Cutting Cafeteria Costs
Case 3.3 Staffing a Call Center
Case 3.4 Promoting a Breakfast
CHAPTER 4 Solving Linear Programming Problems: The Simplex Method
4.1 The Essence of the Simplex Method
4.2 Setting Up the Simplex Method
4.3 The Algebra of the Simplex Method
4.4 The Simplex Method in Tabular Form
4.5 Tie Breaking in the Simplex Method
4.6 Adapting to Other Model Forms
4.7 Postoptimality Analysis
4.8 Computer Implementation
4.9 The Interior-Point Approach to Solving Linear Programming Problems
4.10 Conclusions
Appendix 4.1 An Introduction to Using LINDO and LINGO
Selected References
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Problems
Case 4.1 Fabrics and Fall Fashions
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Case 4.2 New Frontiers
Case 4.3 Assigning Students to Schools
CHAPTER 5 The Theory of the Simplex Method
5.1 Foundations of the Simplex Method
5.2 The Simplex Method in Matrix Form
5.3 A Fundamental Insight
5.4 The Revised Simplex Method
5.5 Conclusions
Selected References
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Problems
CHAPTER 6 Duality Theory and Sensitivity Analysis
6.1 The Essence of Duality Theory
6.2 Economic Interpretation of Duality
6.3 Primal–Dual Relationships
6.4 Adapting to Other Primal Forms
6.5 The Role of Duality Theory in Sensitivity Analysis
6.6 The Essence of Sensitivity Analysis
6.7 Applying Sensitivity Analysis
6.8 Performing Sensitivity Analysis on a Spreadsheet
6.9 Conclusions
Selected References
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Problems
Case 6.1 Controlling Air Pollution
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Case 6.2 Farm Management
Case 6.3 Assigning Students to Schools, Revisited
Case 6.4 Writing a Nontechnical Memo
CHAPTER 7 Other Algorithms for Linear Programming
7.1 The Dual Simplex Method
7.2 Parametric Linear Programming
7.3 The Upper Bound Technique
7.4 An Interior-Point Algorithm
7.5 Conclusions
Selected References
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Problems
CHAPTER 8 The Transportation and Assignment Problems
8.1 The Transportation Problem
8.2 A Streamlined Simplex Method for the Transportation Problem
8.3 The Assignment Problem
8.4 A Special Algorithm for the Assignment Problem
8.5 Conclusions
Selected References
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Problems
Case 8.1 Shipping Wood to Market
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Case 8.2 Continuation of the Texago Case Study
Case 8.3 Project Pickings
CHAPTER 9 Network Optimization Models
9.1 Prototype Example
9.2 The Terminology of Networks
9.3 The Shortest-Path Problem
9.4 The Minimum Spanning Tree Problem
9.5 The Maximum Flow Problem
9.6 The Minimum Cost Flow Problem
9.7 The Network Simplex Method
9.8 A Network Model for Optimizing a Project’s Time-Cost Trade-Off
9.9 Conclusions
Selected References
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Problems
Case 9.1 Money in Motion
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Case 9.2 Aiding Allies
Case 9.3 Steps to Success
CHAPTER 10 Dynamic Programming
10.1 A Prototype Example for Dynamic Programming
10.2 Characteristics of Dynamic Programming Problems
10.3 Deterministic Dynamic Programming
10.4 Probabilistic Dynamic Programming
10.5 Conclusions
Selected References
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Problems
CHAPTER 11 Integer Programming
11.1 Prototype Example
11.2 Some BIP Applications
11.3 Innovative Uses of Binary Variables in Model Formulation
11.4 Some Formulation Examples
11.5 Some Perspectives on Solving Integer Programming Problems
11.6 The Branch-and-Bound Technique and Its Application to Binary Integer Programming
11.7 A Branch-and-Bound Algorithm for Mixed Integer Programming
11.8 The Branch-and-Cut Approach to Solving BIP Problems
11.9 The Incorporation of Constraint Programming
11.10 Conclusions
Selected References
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Problems
Case 11.1 Capacity Concerns
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Case 11.2 Assigning Art
Case 11.3 Stocking Sets
Case 11.4 Assigning Students to Schools, Revisited Again
CHAPTER 12 Nonlinear Programming
12.1 Sample Applications
12.2 Graphical Illustration of Nonlinear Programming Problems
12.3 Types of Nonlinear Programming Problems
12.4 One-Variable Unconstrained Optimization
12.5 Multivariable Unconstrained Optimization
12.6 The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization
12.7 Quadratic Programming
12.8 Separable Programming
12.9 Convex Programming
12.10 Nonconvex Programming (with Spreadsheets)
12.11 Conclusions
Selected References
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Problems
Case 12.1 Savvy Stock Selection
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Case 12.2 International Investments
Case 12.3 Promoting a Breakfast Cereal, Revisited
CHAPTER 13 Metaheuristics
13.1 The Nature of Metaheuristics
13.2 Tabu Search
13.3 Simulated Annealing
13.4 Genetic Algorithms
13.5 Conclusions
Selected References
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Problems
CHAPTER 14 Game Theory
14.1 The Formulation of Two-Person, Zero-Sum Games
14.2 Solving Simple Games—A Prototype Example
14.3 Games with Mixed Strategies
14.4 Graphical Solution Procedure
14.5 Solving by Linear Programming
14.6 Extensions
14.7 Conclusions
Selected References
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Problems
CHAPTER 15 Decision Analysis
15.1 A Prototype Example
15.2 Decision Making without Experimentation
15.3 Decision Making with Experimentation
15.4 Decision Trees
15.5 Using Spreadsheets to Perform Sensitivity Analysis on Decision Trees
15.6 Utility Theory
15.7 The Practical Application of Decision Analysis
15.8 Conclusions
Selected References
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Problems
Case 15.1 Brainy Business
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Case 15.2 Smart Steering Support
Case 15.3 Who Wants to be a Millionaire?
Case 15.4 University Toys and the Engineering Professor Action Figures
CHAPTER 16 Markov Chains
16.1 Stochastic Processes
16.2 Markov Chains
16.3 Chapman-Kolmogorov Equations
16.4 Classification of States of a Markov Chain
16.5 Long-Run Properties of Markov Chains
16.6 First Passage Times
16.7 Absorbing States
16.8 Continuous Time Markov Chains
Selected References
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Problems
CHAPTER 17 Queueing Theory
17.1 Prototype Example
17.2 Basic Structure of Queueing Models
17.3 Examples of Real Queueing Systems
17.4 The Role of the Exponential Distribution
17.5 The Birth-and-Death Process
17.6 Queueing Models Based on the Birth-and-Death Process
17.7 Queueing Models Involving Nonexponential Distributions
17.8 Priority-Discipline Queueing Models
17.9 Queueing Networks
17.10 The Application of Queueing Theory
17.11 Conclusions
Selected References
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Problems
Case 17.1 Reducing In-Process Inventory
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Case 17.2 Queueing Quandary
CHAPTER 18 Inventory Theory
18.1 Examples
18.2 Components of Inventory Models
18.3 Deterministic Continuous-Review Models
18.4 A Deterministic Periodic-Review Model
18.5 Deterministic Multiechelon Inventory Models for Supply Chain Management
18.6 A Stochastic Continuous-Review Model
18.7 A Stochastic Single-Period Model for Perishable Products
18.8 Revenue Management
18.9 Conclusions
Selected References
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Problems
Case 18.1 Brushing Up on Inventory Control
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Case 18.2 TNT: Tackling Newsboy’s Teachings
Case 18.3 Jettisoning Surplus Stock
CHAPTER 19 Markov Decision Processes
19.1 A Prototype Example
19.2 A Model for Markov Decision Processes
19.3 Linear Programming and Optimal Policies
19.4 Policy Improvement Algorithm for Finding Optimal Policies
19.5 Discounted Cost Criterion
19.6 Conclusions
Selected References
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Problems
CHAPTER 20 Simulation
20.1 The Essence of Simulation
20.2 Some Common Types of Applications of Simulation
20.3 Generation of Random Numbers
20.4 Generation of Random Observations from a Probability Distribution
20.5 Outline of a Major Simulation Study
20.6 Performing Simulations on Spreadsheets
20.7 Conclusions
Selected References
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Problems
Case 20.1 Reducing In-Process Inventory, Revisited
Case 20.2 Action Adventures
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Case 20.3 Planning Planers
Case 20.4 Pricing under Pressure
APPENDIXES
1. Documentation for the OR Courseware
2. Convexity
3. Classical Optimization Methods
4. Matrices and Matrix Operations
5. Table for a Normal Distribution
PARTIAL ANSWERS TO SELECTED PROBLEMS
INDEXES
Author Index
Subject Index
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